Our algorithm FW-smoothing (Alg. REF ) for minimizing \(f\)  uses the Frank-Wolfe method for nonsmooth optimization from [1]}[1]} uses the smoothing scheme of [3]} which is in fact equal to the Moreau envelope (see [4]}).. Given a sequence \((\beta _t)_{t\ge 1}\)  of positive values decreasing to 0, the algorithm constructs iterates \(P^{(t)}\)  by applying Frank-Wolfe updates to \(f^{\beta _t}\)  at each iteration \(t\) . More precisely, FW-smoothing finds an update direction with respect
to \(\nabla f^{\beta _t}\)  by computing:
\(&Q^{(t)}= _{P\in \mathcal {P}} {P}{\nabla f^{\beta _t}(P^{(t-1)})}.\) 
